Erika and Kitty, who are twins, just received $30,000 each for their 25th birthd
ID: 2663070 • Letter: E
Question
Erika and Kitty, who are twins, just received $30,000 each for their 25th birthday. They both have aspirations to become millionaires. Each plans to make a $5,000 annual contribution to her “early retirement fund” on her birthday, beginning a year from today. Erika opened an account with the Safety First Bond Fund, a mutual fund that invests in high- quality bonds whose investors have earned 6% per year in the past. Kitty invested in the New Issue Bio-Tech Fund, which invests in small, newly issued bio-tech stocks and whose investors have earned an average of 20% per year in the fund’s relatively short history.a. If the two women’s fund earn the same returns in the future as in the past, how old will each be when she becomes a millionaire?
b. How large would Erika’s annual contributions have to be for her to become a millionaire at the same age as Kitty, assuming their expected returns are realized?
c. Is it rational or irrational for Erika to invest in the bond fund rather than in stocks
Explanation / Answer
Calculating the number of years to make Erika a millionaire: Step1: Go to excel and click "insert" to insert the function Step2: select the "NPer" function as we are finding the number of years in this case. Step3: Enter the values as Rate = 6%; PMT = -5000; PV = 30000; FV = -1,000,000 Step4: Click "OK" to get the desired value. The value comes to "38.7" Therefore , it takes 38 yrs for Erika to become a millionaire. Calculating the number of years to make Ketty a millionaire: Step1: Go to excel and click "insert" to insert the function Step2: select the "NPer" function as we are finding the number of years in this case. Step3: Enter the values as Rate = 20%; PMT = -5000; PV = 30000; FV = -1,000,000 Step4: Click "OK" to get the desired value. The value comes to "16" Therefore , it takes 16yrs for Ketty to become a millionaire. b) Calculating the annual contribution of Erika at the same age as Ketty: Step1: Go to excel and click "insert" to insert the function Step2: select the "PMT" function as we are finding the annual contribution in this case. Step3: Enter the values as Rate = 6%; Nper = 16; PV = 30000; FV = -1000000 Step4: Click "OK" to get the desired value. The value comes to "$35,983" Therefore, Erika should contribute $35,983 each year until 16yrs to become a millionaire like Ketty. c) Though the bond funds earns an average of 6% per year which is less than the Ketty's required rate of return, yet it is relevant because the future returns can be forecasted from the past returns. We know that the lower the return, the lower the risk of loosing money. Bonds are safer than stocks because they can also be issued by government also called government bonds which are less likely to default than corporate bonds because government entities are less likely to suffer bankruptcy than firms are, as they can draw on tax revenue or even raise taxes to satisfy the debt obligation.
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